A fractal approach to the diffusion process of red ink in a saline water

Abstract

The diffusion of the red ink in saline water is completely stochastic and highly unpredictable, and no differential model can precisely describe the process. This paper elucidates that the diffusion takes place in a molecule scale, therefore, the continuum assumption in fluid mechanics becomes totally invalid, and the two-scale fractal calculus has to be adopted to take into account the effects of the particles? size in the red ink and the properties of the saline solution including its concentration, water molecule?s size and distribution on the diffusion process. On the molecule?s scale, the diffusion becomes completely deterministic and predictable. An experiment is carefully designed and some phenomena, including optical observation and highly selective diffusion routine, are theoretically explained. This paper sheds light on modeling various contamination diffusion in air and water.